Convert 111 111 011 109 703 to a Signed Binary in One's (1's) Complement Representation

How to convert decimal number 111 111 011 109 703(10) to a signed binary in one's (1's) complement representation

What are the steps to convert decimal number
111 111 011 109 703 to a signed binary in one's (1's) complement representation?

  • A signed integer, written in base ten, or a decimal system number, is a number written using the digits 0 through 9 and the sign, which can be positive (+) or negative (-). If positive, the sign is usually not written. A number written in base two, or binary, is a number written using only the digits 0 and 1.

1. Divide the number repeatedly by 2:

Keep track of each remainder.

Stop when you get a quotient that is equal to zero.


  • division = quotient + remainder;
  • 111 111 011 109 703 ÷ 2 = 55 555 505 554 851 + 1;
  • 55 555 505 554 851 ÷ 2 = 27 777 752 777 425 + 1;
  • 27 777 752 777 425 ÷ 2 = 13 888 876 388 712 + 1;
  • 13 888 876 388 712 ÷ 2 = 6 944 438 194 356 + 0;
  • 6 944 438 194 356 ÷ 2 = 3 472 219 097 178 + 0;
  • 3 472 219 097 178 ÷ 2 = 1 736 109 548 589 + 0;
  • 1 736 109 548 589 ÷ 2 = 868 054 774 294 + 1;
  • 868 054 774 294 ÷ 2 = 434 027 387 147 + 0;
  • 434 027 387 147 ÷ 2 = 217 013 693 573 + 1;
  • 217 013 693 573 ÷ 2 = 108 506 846 786 + 1;
  • 108 506 846 786 ÷ 2 = 54 253 423 393 + 0;
  • 54 253 423 393 ÷ 2 = 27 126 711 696 + 1;
  • 27 126 711 696 ÷ 2 = 13 563 355 848 + 0;
  • 13 563 355 848 ÷ 2 = 6 781 677 924 + 0;
  • 6 781 677 924 ÷ 2 = 3 390 838 962 + 0;
  • 3 390 838 962 ÷ 2 = 1 695 419 481 + 0;
  • 1 695 419 481 ÷ 2 = 847 709 740 + 1;
  • 847 709 740 ÷ 2 = 423 854 870 + 0;
  • 423 854 870 ÷ 2 = 211 927 435 + 0;
  • 211 927 435 ÷ 2 = 105 963 717 + 1;
  • 105 963 717 ÷ 2 = 52 981 858 + 1;
  • 52 981 858 ÷ 2 = 26 490 929 + 0;
  • 26 490 929 ÷ 2 = 13 245 464 + 1;
  • 13 245 464 ÷ 2 = 6 622 732 + 0;
  • 6 622 732 ÷ 2 = 3 311 366 + 0;
  • 3 311 366 ÷ 2 = 1 655 683 + 0;
  • 1 655 683 ÷ 2 = 827 841 + 1;
  • 827 841 ÷ 2 = 413 920 + 1;
  • 413 920 ÷ 2 = 206 960 + 0;
  • 206 960 ÷ 2 = 103 480 + 0;
  • 103 480 ÷ 2 = 51 740 + 0;
  • 51 740 ÷ 2 = 25 870 + 0;
  • 25 870 ÷ 2 = 12 935 + 0;
  • 12 935 ÷ 2 = 6 467 + 1;
  • 6 467 ÷ 2 = 3 233 + 1;
  • 3 233 ÷ 2 = 1 616 + 1;
  • 1 616 ÷ 2 = 808 + 0;
  • 808 ÷ 2 = 404 + 0;
  • 404 ÷ 2 = 202 + 0;
  • 202 ÷ 2 = 101 + 0;
  • 101 ÷ 2 = 50 + 1;
  • 50 ÷ 2 = 25 + 0;
  • 25 ÷ 2 = 12 + 1;
  • 12 ÷ 2 = 6 + 0;
  • 6 ÷ 2 = 3 + 0;
  • 3 ÷ 2 = 1 + 1;
  • 1 ÷ 2 = 0 + 1;

2. Construct the base 2 representation of the positive number:

Take all the remainders starting from the bottom of the list constructed above.

111 111 011 109 703(10) = 110 0101 0000 1110 0000 1100 0101 1001 0000 1011 0100 0111(2)

3. Determine the signed binary number bit length:

  • The base 2 number's actual length, in bits: 47.

  • A signed binary's bit length must be equal to a power of 2, as of:
  • 21 = 2; 22 = 4; 23 = 8; 24 = 16; 25 = 32; 26 = 64; ...
  • The first bit (the leftmost) indicates the sign:
  • 0 = positive integer number, 1 = negative integer number

The least number that is:

1) a power of 2

2) and is larger than the actual length, 47,

3) so that the first bit (leftmost) could be zero
(we deal with a positive number at this moment)

=== is: 64.


4. Get the positive binary computer representation on 64 bits (8 Bytes):

If needed, add extra 0s in front (to the left) of the base 2 number, up to the required length, 64.


Decimal Number 111 111 011 109 703(10) converted to signed binary in one's complement representation:

111 111 011 109 703(10) = 0000 0000 0000 0000 0110 0101 0000 1110 0000 1100 0101 1001 0000 1011 0100 0111

Spaces were used to group digits: for binary, by 4, for decimal, by 3.

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How to convert signed integers from the decimal system to signed binary in one's complement representation

Follow the steps below to convert a signed base 10 integer number to signed binary in one's complement representation:

  • 1. If the number to be converted is negative, start with the positive version of the number.
  • 2. Divide repeatedly by 2 the positive representation of the integer number that is to be converted to binary, keeping track of each remainder, until we get a quotient that is equal to ZERO.
  • 3. Construct the base 2 representation of the positive number, by taking all the remainders starting from the bottom of the list constructed above. Thus, the last remainder of the divisions becomes the first symbol (the leftmost) of the base two number, while the first remainder becomes the last symbol (the rightmost).
  • 4. Binary numbers represented in computer language must have 4, 8, 16, 32, 64, ... bit length (a power of 2) - if needed, fill in '0' bits in front (to the left) of the base 2 number calculated above, up to the right length; this way the first bit (leftmost) will always be '0', correctly representing a positive number.
  • 5. To get the negative integer number representation in signed binary one's complement, replace all '0' bits with '1's and all '1' bits with '0's.

Example: convert the negative number -49 from the decimal system (base ten) to signed binary one's complement:

  • 1. Start with the positive version of the number: |-49| = 49
  • 2. Divide repeatedly 49 by 2, keeping track of each remainder:
    • division = quotient + remainder
    • 49 ÷ 2 = 24 + 1
    • 24 ÷ 2 = 12 + 0
    • 12 ÷ 2 = 6 + 0
    • 6 ÷ 2 = 3 + 0
    • 3 ÷ 2 = 1 + 1
    • 1 ÷ 2 = 0 + 1
  • 3. Construct the base 2 representation of the positive number, by taking all the remainders starting from the bottom of the list constructed above:
    49(10) = 11 0001(2)
  • 4. The actual bit length of base 2 representation is 6, so the positive binary computer representation of a signed binary will take in this case 8 bits (the least power of 2 that is larger than 6) - add '0's in front of the base 2 number, up to the required length:
    49(10) = 0011 0001(2)
  • 5. To get the negative integer number representation in signed binary one's complement, replace all '0' bits with '1's and all '1' bits with '0's:
    -49(10) = 1100 1110
  • Number -49(10), signed integer, converted from the decimal system (base 10) to signed binary in one's complement representation = 1100 1110